00860nam--2200337---450 99000272584020331620220601120951.0000272584USA01000272584(ALEPH)000272584USA0100027258420060328d1991----km-y0itay0103----bafreFR-|||||||001yy<<L'>> esquiveNicolas FlorenceParisLe milieu du jour[copyr. 1991]62 p.20 cm.20012001001-------2001843.914FLORENCE,Nicolas592873ITsalbcISBD990002725840203316XV.4.A. 240F.F.XV.4.BKUMASENATORE9020060328USA011735Esquive1000598UNISA03827nam 2200517 450 991048558590332120230622200746.03-030-76959-3(CKB)5590000000503304(MiAaPQ)EBC6676264(Au-PeEL)EBL6676264(OCoLC)1258366109(PPN)259391182(EXLCZ)99559000000050330420220326d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe logical syntax of Greek mathematics /Fabio AcerbiCham, Switzerland :Springer,[2021]©20211 online resource (401 pages)Sources and studies in the history of mathematics and physical sciences3-030-76958-5 Includes bibliographical references and index.Intro -- TABLE OF CONTENTS -- LIMINALIA -- 1. THE THREE STYLISTIC CODES OF GREEK MATHEMATICS -- 1.1. THE DEMONSTRATIVE CODE -- 1.2. THE PROCEDURAL CODE -- 1.3. THE ALGORITHMIC CODE -- 1.4. PUNCTUATING GREEK MATHEMATICAL TEXTS -- 1.5. THE ELEMENTS AND ITS LEXICAL CONTENT -- 2. VALIDATION AND TEMPLATES -- 2.1. ARISTOTLE AND GALEN ON LINGUISTIC TEMPLATES -- 2.2. SUBSENTENTIAL VALIDATION: FORMULAIC TEMPLATES -- 2.3. SENTENTIAL VALIDATION: SYNTACTIC TEMPLATES -- 2.4. LARGE-SCALE VALIDATION: ANALYSIS AND SYNTHESIS -- 2.4.1. Geometric analysis and synthesis -- 2.4.2. Validating algorithms and procedures by the "givens" -- 3. THE PROBLEM OF MATHEMATICAL GENERALITY -- 3.1. THE PRESENTIAL VALUE OF THE VERB "TO BE" IN THE SETTING-OUT -- 3.2. THE FUNCTION OF THE DENOTATIVE LETTERS -- 3.3. THE INDEFINITE STRUCTURE -- 3.4. ONTOLOGICAL COMMITMENT -- 3.5. OVERSYMMETRIZED DIAGRAMS -- 4. THE DEDUCTIVE MACHINE -- 4.1. ENUNCIATION AND CONCLUSION -- 4.2. SUPPOSITIONS AND "SETTING-OUT" -- 4.2.1. Determination -- 4.3. THE ROLE OF CONSTRUCTIONS -- 4.4. ANAPHORA -- 4.5. PROOF -- 4.5.1. The logic of relations -- 4.5.2. Metamathematical markers: potential and analogical proofs, references to the obvious, optative mood, personal verb forms -- 4.5.3. Postposed arguments -- 4.5.4. Instantiated and non-instantiated citations of theorems -- 4.5.5. Assumptions and coassumptions -- 5. THE LOGICAL SYNTAX -- 5.1. QUANTIFICATION -- IMPLICIT AND EXPLICIT GENERALITY -- 5.1.1. Quantifiers -- 5.1.2. Determiners of arbitrariness -- 5.1.3. Determiners of indefiniteness -- 5.1.4. Generalizing qualifiers -- 5.1.5. The use of the article -- 5.1.6. Ordinals as variables -- 5.1.7. The indefinite conditionals of Stoic logic -- 5.2. MODALS -- 5.2.1. Reductions to the impossible -- 5.2.2. Arguments "for a contrapositive" -- 5.3. SENTENTIAL OPERATORS -- 5.3.1. Conditional -- 5.3.2. Paraconditional.5.3.3. Negation -- 5.3.4. Disjunction -- 5.3.5. Conjunction -- 5.3.6. Syllogistic connectors -- APPENDICES -- APPENDIX A. PROBLEMS IN THE GREEK MATHEMATICAL CORPUS -- APPENDIX B. THEOREMS OF THE DATA THAT HAVE A SYNTHETIC COUNTERPART AND EXTANT SOURCES ON GREEK ANALYSIS AND SYNTHESIS -- APPENDIX C. ONOMASTICON -- BIBLIOGRAPHY -- INDICES -- INDEX NOMINUM -- INDEX FONTIUM -- INDEX LOCORUM -- INDEX RERUM.Sources and studies in the history of mathematics and physical sciences.Mathematics, GreekMatemàtica gregathubHistòriathubLlibres electrònicsthubMathematics, Greek.Matemàtica gregaHistòria510.938Acerbi Fabio611846MiAaPQMiAaPQMiAaPQBOOK9910485585903321The Logical Syntax of Greek Mathematics1985022UNINA